Lie Groups, Lie Algebras, Cohomology and some Applications in Physics [Paperback]

A self-contained introduction to the cohomology theory of Lie groups and some of its applications in physics.This book provides a self-contained introduction to the cohomology theory of Lie groups and algebras and to some of its applications in physics. The topics treated include the differential geometry and extensions of Lie groups, fibre bundles and connections, characteristic classes, index theorem, monopoles, instantons, supersymmetry, Chevalley-Eilenberg approach to Lie algebra cohomology, symplectic cohomology, jet-bundle approach to variational principles in mechanics, Wess-Zumino-Witten terms, infinite Lie algebras, the cohomological descent in mechanics and in gauge theories and anomalies.This book provides a self-contained introduction to the cohomology theory of Lie groups and algebras and to some of its applications in physics. The topics treated include the differential geometry and extensions of Lie groups, fibre bundles and connections, characteristic classes, index theorem, monopoles, instantons, supersymmetry, Chevalley-Eilenberg approach to Lie algebra cohomology, symplectic cohomology, jet-bundle approach to variational principles in mechanics, Wess-Zumino-Witten terms, infinite Lie algebras, the cohomological descent in mechanics and in gauge theories and anomalies.Now in paperback, this book provides a self-contained introduction to the cohomology theory of Lie groups and algebras and to some of its applications in physics. No previous knowledge of the mathematical theory is assumed beyond some notions of Cartan calculus and differential geometry (which are nevertheless reviewed in the book in detail). The examples, of current interest, are intended to clarify certain mathematical aspects and to show their usefulness in physical problems. The topics treated include the differential geometry of Lie groups, fiber bundles and connections, characteristic classes, index theorems, monopoles, instantons, extensions of Lie groups and algebras, some aló$